I had a similar situation recently and drafted the following, although didn't in the end have to use it. It may be useful:
[Signage saying] that restrictions apply in School term times. This is proscribed by Regulation 6 and Schedule 18 of the TSRGD by reason of omission. Such a period is not one of the permitted expressions in para 5 of Part 1 of Schedule 18. In plain English, a driver cannot be expected to know what school term dates are. He might have a good idea that the middle of November, say, is term time but not on which precise date at the beginning of July the summer holidays will start.
So there are particular types of notice that ARE permitted according to the TSRGD, such as "Match Days only" but there is no mention of "Term Times only" and as the list must be read as prescriptive, this implies that any other type of exception signage must not be permitted, i.e. proscribed. I note that you have picked up the TSRGD reference in your re-draft OP.
My particular "offence" was committed on 2 July and the term dates for the public school just up the road, which as a matter of fact I attended many years ago, have the school holidays starting on 4 July. So who is to say whether term dates are only for state schools of the borough in which they are located? Public (which of course means private!) schools are also schools and have term times and holiday times.